Which of the following numbers is a factor of 126? ${4,5,9,12,13}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $126$ by each of our answer choices. $126 \div 4 = 31\text{ R }2$ $126 \div 5 = 25\text{ R }1$ $126 \div 9 = 14$ $126 \div 12 = 10\text{ R }6$ $126 \div 13 = 9\text{ R }9$ The only answer choice that divides into $126$ with no remainder is $9$ $ 14$ $9$ $126$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $126$ $126 = 2\times3\times3\times7 9 = 3\times3$ Therefore the only factor of $126$ out of our choices is $9$. We can say that $126$ is divisible by $9$.